Question

$△ABC\cong △$DEF.
What is the measure of $\angle F?$

• A. 70${}^{\circ }$
• B. 60${}^{\circ }$
• C. 50${}^{\circ }$
• D. 40${}^{\circ }$

Answer 1

The correct option is A 70${}^{\circ }$

Since, the given two triangles are congruent, corresponding parts are equal.
$\Rightarrow$ corresponding parts:
AC = DF, CB = FE, BA = ED
and,
$\angle A=\angle D={60}^{\circ }$
$\angle C=\angle F$
$\angle B=\angle E={50}^{\circ }$

In $△DEF$
$\angle D={60}^{\circ }$
$\angle E={50}^{\circ }$
$\therefore \angle F={180}^{\circ }-\angle D+\angle E$ (sum of all the internal angles of a triangle is 180${}^{\circ }$)
$\Rightarrow \angle F={180}^{\circ }-({60}^{\circ }+{50}^{\circ })$
$\Rightarrow \angle F={180}^{\circ }-\left({110}^{\circ }\right)$
$\Rightarrow \angle F={70}^{\circ }$